The goal of fase is to fit a “Functional Adjacency Spectral Embedding” to an indexed collection of network snapshots. The behavior of each node is summarized by a latent process, which is fit in a prespecifed spline basis. The fase package has options to fit either B-spline (with equally spaced knots) or smoothing spline latent processes. For more details, see MacDonald et al., (2022+).

Additional functions are included in this package to do Procrustes alignments of latent processes stored as 3-dimensional arrays.

You can install fase from CRAN with:

install.packages("fase")

This is a basic example which shows you how to generate functional network data and fit a functional adjacency spectral embedding.

First, we generate $50$ snapshots of a functional network on $100$ nodes, with Gaussian edges (standard deviation $\sigma=4$) and two-dimensional sinusoidal latent processes.

# load fase package
library(fase)
# set a seed
set.seed(1)
# generate functional network data
data <- gaussian_snapshot_ss(n=100,d=2,
                             x_vec=seq(0,1,length.out=50),
                             self_loops=FALSE,
                             sigma_edge=4)

Then we fit a two-dimensional functional adjacency spectral embedding to this data, using a $B$-spline basis design with dimension $9$. This choice of basis dimension is chosen to minimize the network generalized cross validation criterion.

As a post-processing step, and due to the intrinsic non-identifiability of the latent processes, we align our embedding to the original processes used to fit the data. Note that by using proc_align3 (rather than proc_align_slicewise3), we apply the same orthogonal transformation to all the evaluations of the latent process snapshots. The difference between slicewise and common identifying transformations is discussed in more detail in MacDonald et al., (2022+), Appendix C.

# embed with fase (B-spline design)
fit <- fase(data$A,d=2,self_loops=FALSE,
            spline_design=list(type='bs',q=9,x_vec=data$spline_design$x_vec))
# align fitted and true latent processes
Z_align <- proc_align3(fit$Z,data$Z)

Finally, we extract a couple of example estimated (and aligned) latent processes: the first dimension for node 34, and the second dimension for node 54. We plot them against the true values over the entire index space.